Dr. Eick's Graduate AI-class (COSC 6368)

available points: 210 points

homework 3: problems 11, 12, 13, 14, 15.

recommendation: do problems 11 and 12 prior to the midterm exam, and start working on problem 13 prior to the midterm exam.

homework 4: problems 9, 16, 17, 18

last updated: November 19, 11:43a

11) **Probability** (paper and pencil --- 7 points)

Textbook problem 14.4

12) **Bayes Theorem** (paper and pencil --- 5 points)

a)The following predicates are given:

Rain:= "It will rain tommorow"

Cloudy:= "The sky is cloudy today"

Humid:= "It is humid today"

Cold:= "it is cold today"

Moreover, P(Rain)= 0.1
P(Cloudy|Rain)=0.8
P(Humid|Rain)=0.9
P(Cold|Rain)=0.2
P(Cloudy)=0.6
P(Humid)=0.8
P(Cold)=0.4

Will it (usually) rain tomorrow --- compute:

$P(Rain|Cloudy and Humid and Cold) and

P(Rain|Cloudy and Humid)

b) Bayes's theorem is usually applied making the so called
conditional indepence. Explain the assumption
**by referring to the example a** (explain
what what was assumed to be independent in your solution
of problem a).

13)

Solve the Telescope Problem (problem 15.3 of the textbook)! Give reasons for your answers when responding to questions a-e of problem 15.3! There is also a typo: d. suppose M1=1 and M2=3...

Additionally, assume that the probabilty of a telescope being out of focus is 0.02, and that the probability of overcounting by one star is 0.05 and that the probability of undercounting by one star is 0.05; moreover, restrict you analysis to the case that N is limited to 0, 1, 2, 3, or 4 stars! If there are any probabilities missing, just assume that they are evenly distributed (with respect to the set of states they might be in)!

14) **Belief Networks --- Getting the Numbers right!** (Belief Network Development &
Constraint Satisfaction -- 52 Points)
Assume a belief network with a particular structure is given for
Huntington disease. Furthermore the following constraints have
been provided (for details see
Wordfile that contains
the network structure and the constraints;
Wordfile with Constraints of HD-GBBN only) with
respect to the assumed belief network structure. This
knowledge has been been obtained through extraction from
a Huntington
Disease Profile and through interviewing
domain experts. Provide probability tables for the given
belief network structure
(using Netica or any other belief network tool) that implements those
constraints correctly.
Submit the results of running your belief network for the
following cases:

a) nothing is known

b) patient has Chorea

c) test showed CAG-repeat is 44

d) test showed CAG-repeat of 60 and psychiatric disturbances

e) patent has psychiatric disturbances and abnormalities in Cognition

f) patient has positive family history and has been symptom free and is
48 years old.

Write a 1-page report that briefly discusses how you solved the
problem. In summary, you submit a 1-page report, your belief network,
and the answers your belief network provided for questions a-f

15) **RETE Algorithm** (Paper and Pencil ---- 19 points)

a) Give the RETE-network for the following CLIPS-rule (there
was a line cut of in b); the changed part
is red color):

(defrule Santa (P ?x ?y 2) (Q ?y 3) (R ?x 3 ?z) => ...)

b) Assume that the working memory contains: (P 2 2 2) (P 2 3 2) (Q 3 3) (Q 7 3) (Q 2 3) (Q 2 4) (R 2 3 7) (R 3 3 7). Indicate the tokens that are stored in each node of the network.

c) Assume (P 3 2 2) is inserted into the working memory. Which computations have to be done, when the RETE algorithms is used?

d) Assume now (Q 2 3) is removed from the working memory. Which computations have to be done, when the RETE-algorithm is used.

e) If the conditions of the Santa-Rule would be reordered; would your answer to questions c) and d) change?

f) What are the main ideas of the RETE algorithm? Why is it popular for implementing forward chaining rule-based systems?

16) ** Decision Trees ** (Paper and Pencil --- 14 points)

Construct the decision tree C4.5 would generate
for the following dataset (updated on
Nov. 19, 1999):

A1 | A2 | A3 | A4 | Class |
---|---|---|---|---|

0 | 0 | 0 | 0 | C1 |

2 | 0 | 0 | 0 | C1 |

1 | 1 | 0 | 0 | C1 |

1 | 1 | 0 | 0 | C2 |

1 | 1 | 1 | 1 | C2 |

2 | 1 | 1 | 0 | C2 |

2 | 0 | 0 | 1 | C2 |

1 | 1 | 0 | 1 | C2 |

Indicate all computations that resulted in the construction of your submitted tree (especially discuss how the information gain heuristics was used).

17) ** Knowledge Discovery using Decision Trees** (using
a decision tree tool, learning about data analysis and knowledge
discovery --- 66 points)
The goal of this project is to explore how decision tree
tools can help in predicting

- the position of a NBA-player based on other attributes of the player ( NBA-Data Set, NBA-Player Raw Data (XSEL), NBA Player Index --- can be used to check for errors in the data collection)
- the free throw percentage of a player that is defined as being HIGH (82% and more), MEDIUM (at least 71% and less than 82%), and LOW (less than 71%)

18) **Ontologies** (18 points)

Read the *Chadrasekaran&...'s article centering on
ontologies*, and write a 150 word essay
that addresses most of the following questions and
topics (you are allowed to skip
one or two questions/topics):
What reasons does the author give why ontologies are important? Do
you agree with what the author is saying? Is the list of reasons that
the author gives, complete (if no, give other reasons not listed in
the paper).
Give
a list of applications for which ontologies are/might become important ---
also briefly discuss what role ontologies play in the context of the
listed applications.
What kind of ontology tools / ontology
technologies are needed to support these applications?